A Challenging Problem of Decahedron With 10 Congruent Right Kite Faces

Geometry Level 5

The diagram above shows a decahedron that has 10 congruent faces each as a right kite (i.e. a cyclic quadrilateral consisting of two congruent right triangles with common hypotenuse).

It has two pairs of unequal sides \(a,b\) with \(a<b\).

And also has 12 vertices which exactly lie on a spherical surface with certain radius \(R\).

If \(b=15\), then what is the value of radius \(R\)?


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